1
Technical and Economic Aspects of Tripole
HVDC
L. O. Barthold , Fellow, IEEE
Abstract—This paper shows how, with simple modifications
using either conventional or bidirectional valves, bipole and
monopole systems can be connected in parallel and operated as a
three pole configuration in which no earth return current flows
in either normal or pole-out conditions. While slightly less
efficient in terms of equipment utilization, the system reduces
line losses for a given MW transfer and has better overload and
internal redundancy; both of which enhance (n-1)-constrained
loading of the parallel ac system. Because it makes full thermal
use of three conductors, the tripole system improves both the
technical and economic cases for converting existing three-phase
ac lines to dc. Doing so increases power transfer much more than
is possible with compensation or phase shifting transformers.
The paper reviews the basic principles inherent in the tripole
HVDC system and compares characteristics of both bipole and
tripole alternatives in the context of an ac network.
Index Terms-—DC-AC Power Conversion, DC Power
Transmission, DC Power Systems, HVDC Converters, HVDC
Substations, HVDC Transmission, Power Transmission,
Transmission Lines, Transmission Line Theory, Valves.
H
which presumed total loss of an ac circuit, should apply not to
an entire dc line but to one of its poles; the surviving pole
presumably remaining in operation. [1] Those criteria would
benefit further by explicit recognition of dc’s overload and
internal redundancy characteristics, both of which depend on
dc configuration and station design. The analysis presented in
this paper presumes that both system design and reliability
criteria allow full exploitation of HVDC’s characteristics.
II. FUNDAMENTALS OF THE TRIPOLE HVDC SYSTEM.
Figure 1 shows a bipole and monopole systems fed from the
same bus and supplying a common receiving-end bus.
Monopole earth return current is eliminated by two
modifications - both using standard dc system components: (a)
The monopole is equipped with an additional bridge
connected in anti-parallel to the first 1 and (b) All thyristors
and their heat sinks are rated higher than normal.
Transformers and other station equipment are standard, both
in design and rating. [2], [3]
I. INTRODUCTION
VDC links play an important role in powers systems
throughout the world but their potential as an integral
element within ac networks has yet to be fully exploited; In
part because dc depends on communication and programmed
logic to achieve the emergency response benefit that ac
achieves through Kirchoff’s laws. Furthermore reliability
standards, derived largely from ac system operation, have
been slow to adapt to HVDC’s capabilities and characteristics.
As to the first barrier, one need only look to the history of ac
transmission systems to see its demise. AC systems,
dependent to some degree on communication and control at
the outset, have grown steadily more so; witness introduction
of SCADA systems, remedial action schemes (RAS), Special
Protection Schemes (SPS), and the growing acceptance of
FACTS and real time phase angle-based operation logic. In
addition, extensive research is underway on wide area
managements systems (WAMS) to facilitate a “smart grid” to
accommodate ac system weaknesses. As to the second
barrier, it was only recently that NERC and most other
planning groups accepted the fact that ac system N-1 criteria,
.
:
L.O. Barthold, founder and retired Chairman of Power Technologies, Inc.
is an independent transmission Consultant; 10 Woods Point Lane, Lake
George NY USA 12845 (email imod@adelphia.net).
A
+
B
Pole 1
_
Pole 2
+/ _
Pole 3
Figure 1 Parallel bipole and monopole HVDC systems.
Poles 1 and 2 of the “tripole” configuration of fig. 1 are
unidirectional but of opposite polarity. Pole 3 is capable of
reversing both voltage and current. At intermediate levels of
power the three poles would operate as a bipole in which pole
1 carries positive current and poles 2 and 3 share the negative
return current, thus minimizing losses. As power is increased
1
A function that could also make use of bidirectional valves, once
commercially available.
2
pole 1 will reach its thermal rating first - the rating which
poles 1 and 2 could sustain alone. That will be considered 1
pu current and power in subsequent analyses.
Power can be increased above 1 pu power, sustaining the split
return operation described above, by periodically
interchanging high and low current duty as shown in fig. 2.
Imax
V =+1
Imin
0
Pole 1
Pole 2
0
- Imin
V=-1
- Imax
V =+1
(Imax-Imin)
0
I3 = 0
Pole 3
T
- (Imax-Imin)
V=-1
Figure 2 Current-time diagram of current in Poles 1, 2 and 3.
Pole 3 periodically relieves a portion of the current carried by
pole 1 - then a portion of the current carried by pole 3. The
ratio Imax/Imin can be sustained at 2 while power is increased up
to 1.265 times the bipole level. If that ratio is then increased to
3.73, power is equally divided among all three poles and the
total power is 1.37 times the level achievable with just two
conductors and a bipole converter. The tripole/bipole ratio
would be 1.5 but for the form factor of the tripole current.
The period of the high/low current cycle will depend on the
thermal characteristics of line conductors. If made the order of
four or five minutes, conductor temperature excursions will be
a few degrees C above and below what it would be with
constant current of the same root means square value. That
variation is roughly the same as would be seen by normal
changes in wind or cloud cover.
The inset in fig. 2 shows that current ramps can be modest in
slope, e.g. one or two seconds and that ample time can be
allowed to reverse voltage on pole 3. – all with continuous
total power. Comprehensive simulation of the tripole system
on actual configurations, using PSCAD shows no unusual
problems in reactive power requirement, flicker control, or
harmonic generation.
III. OVERLOAD AND REDUNDANCY CHARACTERISTICS
A. Overload Characteristic
It is reasonable to assume an inherent 15% thirty minute
overload capability for both bipole and tripole schemes. The
tripole gains an additional 9% if short term earth return
current is allowed or if corresponding provisions are made
using insulated shield wires. This results from reversion to
classical bipole/monopole operation, thereby increasing form
factor to 1.0 and output from 1.37 to 1.5 prior, prior to
overload. That 9% advantage will increase (n-1)-constrained
loading on parallel ac lines since it allows dc to assume
greater emergency back-up role.
In dynamically constrained ties where high transfers in the 0
to 1 second time frame are important, dc transmission has
important advantages. AC systems develop synchronizing
power only after an angle excursion has developed while dc
can provide synchronizing power virtually the instant it is
prompted by its controls. Furthermore thyristors are generally
capable of 1.5 times overload for the order of one second,
giving dc an advantage in the magnitude of short term
synchronizing power transmittable. Both attributes may
leverage the dc rating by allowing higher flow on parallel ac
lines.[4] Because of its valve rating characteristics, the tripole
can transmit three times more short term (~ 1 second) power
than a bipole sized for the same three-conductor system,
assuming adequate reactive power support in both cases.
B. Internal Redundancy
The continuous rating of a conventional bipole system drops
by 50% after loss of a pole – by 43% if a 15% overload
capability is assumed. This presumes a two conductor system
with either earth or a metallic ground return. If three fully
insulated conductors are available, as with conversion of an ac
line, mechanical switching can restore full bipole capability
assuming the outage is due to the line, not the converter. To
achieve that redundancy the bipole system must go through a
zero power interval in the order of one second; a dynamic
difficulty for some systems.
If a tripole looses either a bridge or line conductor, power
will, in the worst case, drop momentarily from 1.37 to half
value or .685, then ramp to 1.15 assuming overload capability.
That excursion will be somewhat less than 1 second. Earth
return current will flow for a fraction of a second.
The high redundancy of a tripole design means the (1) higher
allowable loading on parallel ac where loss of a dc pole is
limiting or (2) a higher allowable HVDC rating for the same
ac system impact on loss of a pole.
IV. COST PREMIUM
The tripole system will cost more per kW than a bipole of
equal rating since (1) the monopole requires one extra,
reverse polarity bridge, though no other additional station
equipment, (2) At full power Imax = 1.37 will be sustained
for some minutes (“continuous” as far as thyristor ratings are
3
V. CONVERSION OF AC CIRCUITS TO DC
B. DC/AC Loss Ratio
Whether one diverts more load to an underutilized ac circuit
by adding ac equipment or increases its capability by real time
ratings or sag ameliorization measures, losses as a percent of
load will increase proportional to load. This is shown for an
example line by the ac curve in fig. 4; the solid line
Ratio of dc pole
voltage to ac l-g
crest voltage
DC operating current can usually be substantially higher than
ac current. AC current is usually well below the conductor’s
maximum thermal rating because of (n-1) constraints and
limitations in dispatch flexibility. It is reduced in usefulness to
the extent the power factor is less than 1.0. A DC terminal can
usually be rated to match maximum conductor thermal rating
since in parallel ac and dc configurations total path flow will
be determined by the dc’s emergency rating, not its operating
rating. DC operating current would probably be chosen to
optimize losses. Fig. 3 shows a general range of DC to AC
power ratios before considering the effect of dc conversion on
allowable flow on parallel ac circuits.
4.0
1 .5
3.5
Tripole
3.0
2.5
Bipole
1.0
1.5
2.0
1.0
1.5
1.0
0.5
0.0
1.0
0.9
0.8
0.7
0.6
0.5
Ratio of Maximum to Operating ac MVA
Figure 3 Example range of expectations in AC to DC transmission line
conversion.
representing its normal loading limits and the dotted line the
extension to those limits achieved by the above measures. The
lower curves show losses for the same power level following
dc conversion. DC losses, which include terminal losses
equal to 0.85% of power per terminal, are roughly half the ac
values for this case and extend the range of power transfer by
a factor of 1.8 for the bipole case and 2.6 for the tripole case.
60
Ex
Co tens
ph mpe ion
Sa ase nsa by
g A shi tio
me f t i n n ,
lio g o
ra r
t io
n
50
40
30
DC
HV
20
AC
A. DC/AC Power ratio
The DC/AC power ratio is a product of several factors – one
of them voltage. The dc voltage sustainable by an ac line
depends on a number of design issues. In general the
replacement of ac insulators with dc units, a concomitant of
conversion, will result in creepage distance sufficient to at
least sustain a dc voltage equal to line to ground crest ac
voltage. The actual dc voltage limit will also be determined by
clearances, either as found or altered by tower or suspension
system modifications, sag amelioration, etc. Corona effects
may actually be a more important limit to the applicable dc
voltage. Matching both positive and negative poles to line-toground ac crest voltage results in a conductor-to-conductor
voltage of 2.0 rather than 1.73 as in ac; a 15% increase. This
would likely apply to both tripole and bipole conversions
since operating with split return in the bipole case would have
a strong loss incentive and would, in any case, have to be
anticipated during pole-out conditions. A 15% voltage
increase means an increase of about 6% in image-based
electrical gradient for flat configurations.
Losses - MW
Reactive compensation and phase shifting devices are clearly
the least expensive way to increase useful loading on ac
transmission lines of low susceptance/ampacity ratio. DC
achieves a far greater power boost and works for virtually any
susceptance/ampacity ratio. Although expensive, dc
conversion may be justified by eliminating the need for
construction of additional ac circuits and by reduction of
system losses. Its justification depends on several factors.
Ratio of DC MW to AC MW
4.5
10
0
0
100
200
300
400
Tripole Power Limit
The above notwithstanding, the per/kW premium will often be
more than offset by (1) a reduction in the Net Present Value
(NPV) of losses, (2) higher (n-1) constrained loading allowed
on parallel ac circuits, (3) greater dynamic response capability
and (4) in the case of ac to dc conversion, substantially greater
utilization of existing transmission investment.
The dashed curves in fig. 3 show a reasonable range of bipole
conversion expectations and the solid curves the tripole range;
both using the same existing conductor configuration.
Reconductoring the circuit represented by fig. 3 to improve
ampacity, logistically feasible as a part of non-disruptive
conversion, would raise the multiples proportional to the
increase in ampacity.
Bipole Power Limit
concerned) requiring that heat sinks be proportionately
oversized. (For some ratings that factor may also force a move
from 100 mm to 125 mm thyristor elements) and (3) its form
factor of less than unity results in a 9% reduction in useful
MW rating per aggregate rating of equipment.
500
600
700
Real Power Transfer - MW
Figure 4 Comparison of ad and dc losses for equal power levels.
Table 1 shows an example 230 kV case in which it is assumed
that ac measures are taken to extend the ac operating rating of
333 MVA by 15% to 383 MVA which, for a power factor of
0.9, corresponds to 345 MW. Conversion to HVDC assumes
both ac and dc options satisfy the same annual load duration
4
curve. In this example case the loss credit alone may justify
the cost of converter stations irrespective of the major increase
in capability achieved.
AC Voltage
230 kV
DC Voltage
+/-200 kV
Distance
200 kM
Conductor
1,272 kcmil
Resistance
.05 ohms/km
MVA max
514
MVA op
333
DC Rating
345 MW
Discount Rate
2%
Years
Energy Value
Loss Factor
Ann'l AC Loss
Ann'l DC Loss
Loss Savings
Savings
NPV of Savings
Credit/term.
30
$60/MWhr
0.5
121,431 MWh/yr
74,440 MWh/yr
46,991 MWh/yr
$2.9 Mil./yr
$63 Mil.
$94/kW
Table 1 Example NPV of losses for a 230 kV Line.
The discount rate cited in table 1 may actually be conservative
in light of today’s prospective escalation in energy values.
Energy costs ignore the fact that much higher values may
apply during periods when transmission losses are at their
peak.
significantly less than 1.0 may be economically attractive
since the construction cost of a new line is avoided.
B. Strengthening Transmission Supply to a highly developed
Metropolitan area
Transmission in-feeds to high load density areas are often
stretched to their system limits while the receiving system is
already close to the short circuit current capability of station
equipment. Adding a new dc circuit avoids worsening the
short circuit problem. Converting an existing ac circuit to dc
improves it.
The maximum allowable rating of a new in-feed, whether ac
or dc, may be determined by the impact its (n-1) loss has on
an already heavily loaded ac system. The tripole system’s
higher redundancy may allow the system to support a much
higher dc power inflow for the same pole-out impact than
would be the case for a bipole, at least to the point where
second-level reliability criteria become limiting.
VI. ADVANTAGES IN APPLICATION
The advantages in service of the tripole system can best be
illustrated by specific system circumstances. [5]
A. Increasing loading on one of several parallel ac circuits.
If one of several parallel circuits of equal pu susceptance, has
higher ampacity than the rest, selectively reducing its
susceptance by compensation will cause its flow to increase
but force an equal reduction in the flow of parallel lines - at
best simply redistributing loads without increasing (n-1)constrained total path flow. Its ampacity advantage will be of
no use. If that circuit is converted to HVDC, the circuit’s
ampacity multiple will increase a normal ac to dc conversion
advantage of at least 2:1.
C. Making better use of inherent ampacity in long SIL-limited
lines.
It has been shown that DC conversion may be particularly
advantageous where the length of ac lines severely restricts
use of the inherent current-carrying capacity of conductors
whose size is determined by corona issues. [6] Very large
gains in transfer can be achieved within (n-1) constraints by
converting one of several parallel circuits to HVDC while
leaving the others in ac operation.
D. Adding (or converting) a very long line interconnecting
two regions
Several factors may suggest considering the tripole option for
very long inter-regional HVDC links:
i.
The NPV penalty of interrupted power is
proportional to outage exposure which in turn is
proportional to line length. The transmission
investment interrupted by outages is also
proportional to length. The product of these factors
increases the importance of transmission redundancy
for very long lines.
Where several high voltage circuits overlay several
intermediate voltage circuits, all comprising a common
transmission path it may be practical to (a) withdraw one
intermediate voltage circuit from ac operation, serving its
intermediate loads from the others (b) convert the withdrawn
section(s) to an “express” HVDC circuit, (c) reconductor
those sections to make their HVDC capability comparable to
overlying, higher voltage ac circuits.
ii.
Dynamic performance, important for long high
capacity transmission lines connecting two already
synchronous systems, is improved by the tripole’s
high one-second synchronizing power capability.
Where a long tie connects asynchronous systems,
transmission redundancy and overload capability can
effect generation planning decisions in both sending
and receiving systems.
In any dc application, whether new or the result of ac to dc
conversion, the ratio of increase in total path flow to the
terminal rating which achieves that increase may be defined as
DC Effectiveness (DCE). DCE will be higher for new dc
lines than for conversions since, in the latter case, one must
subtract the pre-conversion ac power from whatever level is
achieved by conversion. In the conversion case DCE values
iii.
Since transmission line cost is less than proportionate
to the number of conductors, the tripole circuit may
carry no transmission line cost premium in $/MWkm yet offer a level of redundancy that would
otherwise require two bipole circuits.
The same principle limits the advantage gained by adding an
identical ac circuit in parallel to several others. Higher
ampacity or lower reactance of a new circuit brings no
advantage from an (n-1) perspective. If the new circuit is dc it
can be made to assume a disproportionate share of load
without violating (n-1) criteria.
5
VII. ICE PREVENTION POTENTIAL
Commissioning procedures for conventional Bipole Systems
include periods of “round power” operation during which both
poles assume the same polarity so that full current flows in
both but power is circulated rather than delivered to the load.
Fig. 1 shows that tripole power consists of three magnitude
blocks; one associated with Imax, another with Imin, and a third
with Imax-Imin. Each block is constantly active on one pole or
another so that the power flow associated with any one block
could be selectively reversed by appropriate timing of voltage
polarity reversals. Other forms of modulation can create
additional blocks. Thus it is possible, with the aid of tap
adjustments and limited changes in firing angle, to sustain full
current on all poles while reducing net delivered power from
1.0 to 0. It has recently been shown that doing so will inhibit
ice formation only under mild icing conditions and that about
three times rating is necessary under the worst. [7]
That multiplier is achievable with a recently introduced
scheme based on use of insulated subconductor spacers and
conductor-mounted low-voltage switches to reconnect
subconductors, normally in parallel, into series connection
over regions of ice exposure, thus at least tripling their
current. [8]
VIII. BRUSH FIRE ACCOMMODATION
Brush fires reduce the break-down voltage of transmission
lines both by reducing strength of air clearances and by local
pollution of insulators. DC may have an inherent advantage is
provisions are made for extended voltage reductions. The
tripole system, in particular could (1) sustain an initial pole
flashover with minimal power interruption, (2) reduce voltage
on all poles, (3) restore voltage to the faulted pole (4) repeat
the cycle following progressive flashovers until a voltage was
found low enough to sustain a reduced level of power despite
the fire condition.
IX. UNDERGROUND CABLE IMPLICATIONS
The above arguments differ in several respects for
underground cable systems.
i.
ii.
Where conductors are closely clustered or share a
common heat sink, current is limited by
aggregate rather than individual heat release. This
limits the tripole benefit slightly unless all three
poles are made reversible in voltage and current,
in which case the tripole achieves √2 times the
power that a bipole could achieve using just two
conductors.
DC energization of solid insulation tends to build
up charge within the insulation which, upon
voltage reversal, causes very high local electric
stress. Sufficiently frequent voltage reversals, e.g.
50 Hz, finesse that problem due to the time
constants of charge build-up and migration. It has
iii.
yet to be determined whether reversals of several
minutes will do the same. In any case this
limitation appears to be diminishing with
development of new insulating materials. [9]
The redundancy advantage offered by the tripole
scheme would in most cases be limited to
converter terminal outages inasmuch as most
cable outages are apt to involve all poles.
X. ACKNOWLEDGMENT
The author gratefully acknowledges the technical support
and simulation work of Dr. Dennis Woodford of Electranix,
inc., Harrison K. Clark, Consultant, on system issues, Peter
Lips, Consultant or Thyristor Valve Technology, and The
Electric Power Research Institute (EPRI) for studies of the
Tripole system as a potential application for bidirectional
valves. [10]
XI. REFERENCES
[1] Reliability Standards for the Bulk Electric Systems of North America,
May 2, 2006. North American Electric Reliability Council 116-390
Village Blvd. Princeton, N.J. 08540.
[2] Lionel Barthold, Hartmut Huang, “Conversion of AC Transmission lines
to HVDC using Current Modulation. Inaugural IEEE PES 2005
Conference and Exposition in Africa. Durban, South Africa. 11-15 July,
2005
[3] Lionel O. Barthold "Current Modulation of Direct Current Transmission
Lines" U.S. Patents 6,714,427B1, Mar. 30, 2004
[4] D.A, Woodford “Transmission Upgrading with Synchronous DC Links”
Proceedings of the Future of Power Delivery in the 21st Century, EPRI
Publication TR-109806, May 1998
[5] L.O. Barthold, H.K. Clark, D. Woodford, “Principles and Applications of
Current-Modulated HVDC Transmission Systems”
IEEE T&D
Conference Dallas, Tex. May 21-26, 2006
[6] P. Naidoo, D. Muftic, D. Ijumba, “Investigations into the Upgrading of
Existing HVAC Power Transmission Circuits for Higher Power Transfers
using HVDC Technology” Inaugural IEEE PES 2005 Conference and
Exposition in Africa . Durban, South Africa, 11-15 July 2005
[7] Peter Zsolt, Masoud Farzaneh, Laszlo I. Kiss “Power Line Icing
Prevention by the Joule Effect: parametric analysis and energy
requirements. Proceedings of the International Workshop on Atmospheric
Icing of Structures (IWAIS) June 12-16, 2005 Montreal, Canada.
[8] Pierre Couture “Switching apparatus and method for a segment of an
electric power line” US Patent 6.727,604 B2 Apr. 27 2004
[9] R.Roy, J.K.Nelson,R.K.MacCrone,L.S.Schadler, “Polymer Nanocomposit
Dielectrics – The role of the Interface” IEEE Transactions on Dielectrics
and Electrical Insulation, Vol. 12 No. 4 August, 2005
[10]Bidirectional Valves: Specific Practical Applications of Interest. EPRI,
Palo Alto, CA, and Bonneville Power Administration, Vancouver, WA:
2005: Product ID # 00725.
6
XII. BIOGRAPHY
Lionel O. Barthold (M’1951, F’1965) graduated in
Physics from Northwestern University in 1950.
After various assignments in apparatus and system
transmission engineering, he was named manager
of AC Transmission Engineering for General
Electric’s System Engineering Operation in
Schenectady, NY in 1963. In that capacity he was
also director of Project EHV, a major 500kV
research station, and was instrumental in converting
it to a UHV research facility in 1968.
Barthold founded Power Technologies, Inc. in 1969. Under his leadership PTI
grew to become a leading supplier of high technology consulting services and
software to electric utilities in all parts of the world. He retired from PTI in
1998 and is currently engaged in studies of HVDC conversion of AC
transmission lines.
Active in IEEE’s Power Engineering Society from the earliest days of his
career, Barthold served as president of that society from 1981 to 1983 and is a
recipient of its Power Life Award. He has authored or co-authored 70
technical papers, holds several transmission-related patents, and served on or
chaired numerous technical committees of both IEEE and CIGRE. He was
international chairman of CIGRE’s Study Committee 41 “The Future of
Electric Power and Systems” from 1976 to 1982. Barthold was elected to the
U.S. National Academy of Engineers in 1981